Answer:
C) x = 6, y = 9
Step-by-step explanation:
In the given parallelogram PQRS, the diagonals PR and QS intersect at point T.
Since the diagonals of a parallelogram bisect each other, we have:
[tex]\overline{QT} \cong \overline{TS}[/tex]
[tex]\overline{PT} \cong \overline{TR}[/tex]
Therefore, to find the values of x and y, we can create two equations by substituting the given expressions for each line segment into the congruency equations:
[tex]\begin{cases}3x = 2y\\2x = y + 3\end{cases}[/tex]
Rearrange the second equation to isolate y:
[tex]y = 2x - 3[/tex]
Now, substitute this into the first equation and solve for x:
[tex]3x = 2(2x - 3)\\\\3x = 4x - 6\\\\-x = -6\\\\x = 6[/tex]
Substitute the found value of x into the rearranged second equation and solve for y:
[tex]y=2(6) - 3\\\\y = 12 - 3\\\\y = 9[/tex]
Therefore, the values of x and y are:
[tex]\LARGE\boxed{\boxed{x = 6,\;\;y = 9}}[/tex]
